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Unformatted text preview: HINTS FOR TEACHING CALCULUS WITH APPLICATIONS Algebra Reference Some instructors obtain best results by going through this chapter carefully at the beginning of the semester. Others find it better to refer to it as needed throughout the course. Use whichever method works best for your students. As in the previous edition, we refer to the chapter as a “Reference” rather than a “Review,” and the regular page numbers don’t begin until Chapter 1. We hope this will make your students less anxious if you don’t cover this material. Chapter 1 Instructors sometimes go to either of two extremes in this chapter and the next. Some feel that their students have already covered enough precalculus in high school or in previous courses, and consequently begin with Chapter 3. Unfortunately, if they are wrong, their students may do poorly. Other instructors spend at least half a semester on Chapters 1 and 2 and the algebra reference chapter, and subsequently have little time for calculus. Such a course should not be labeled as calculus. We recommend trying to strike a balance, which may still not make all your students happy. A few may complain that the review of algebra, functions, and graphs is too quick; such students should be sent to a more basic course. Those students who are familiar with this material may become lazy and develop habits that will hurt them later in the course. You may wish to assign a few challenging exercises to keep these students on their toes. Chapter 1 of Calculus with Applications is identical to Chapter 1 of Finite Mathematics and may be skipped by students who have already taken a course using that text. In this edition, we have streamlined the chapter from four to three sections, allowing instructors to reach the calculus material more quickly. Section 1.1 This section and the next may seem fairly basic to students who covered linear functions in high school. Nev- ertheless, many students who have graphed hundreds of lines in their lifetime still lack a thorough understanding of slope, which hampers their understanding of the derivative. Such students could benefit from doing dozens of exercises similar to 39-42. Perpendicular lines are not used in future chapters and could be skipped if you are in a hurry. Section 1.2 Much recent research has been devoted to students’ misunderstandings of the function concept. Such misunder- standings are among the major impediments to learning calculus. One way to help students is to study a simple class of functions first, as we do in this section. In this edition, even more of the general material on functions, including domain and range, is postponed until Chapter 2. Supply and demand provides the students’ first experience with a mathematical model. Spend time developing both the economics and the mathematics involved....
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This note was uploaded on 10/07/2010 for the course CALC 2302 taught by Professor Yuly during the Fall '08 term at University of Texas at Dallas, Richardson.
- Fall '08